Problem on Solving Rational expressions

Topic : Rational Expressions

Problem : Solve 2/x + 5/x²

Solution :
LCM is x²
2/x = 2x/x²
Therefore 2/x + 5/x² = 2x /x² + 5/x² = (2x + 5)/x²
2/x + 5/x² = (2x + 5)/x²

Problem to Find Slope of the tangent line to the Curve

Topic : Slope of tangent line

Question : To Find the Slope of the tangent line to the curve at the given point xy³ - 1y + 1 . 7 = 0 at (- . 7, 1)

Solution :

Linear Equation with Rational co-efficients

Topic : Linear Equations

Question : Solve the system of linear equations.
(2/3) x + (4/5) y = 8
(5/4) x - (3/2) y = - 6

Solution :
(2/3) x + (4/5) y = 8 ------------- (1)
(5/4) x - (3/2) y = - 6 ------------- (2)

To eliminate fractions let us multiply whole equation (1) by 15 and equation (2) by 8
15 *(2/3) x + 15*(4/5) y = 15*8
10x +12y = 120
dividing by 2
5x+6y=60

8*(5/4) x - 8*(3/2) y = - 6*8
10x-12y=-48
divide by 2
5x-6y= -24

So the two equations are
5x+6y=60
5x-6y= -24

adding both the equations
10x = 36
x = 36/10
x=3.6
substituting the value of x in first equation
5x+6y=60
5(3.6)+6y=60
18.0+6y=60
6y=-18.0+60
6y= 42
y = 42/6
y=7

Word Problem on Simple Interest in Banking

Topic : Investments and Simple Interest

Question : Helen Weller invested $15,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the total interest is equal to the interest on the two investments at the rate of 13%?

Solution :

12% of 15000 = 12/100 * 15000
= 1800

Now let the additional money invested be $x.

So 15% of x = 15/100 * x
= 0.15x

Now 13% of (15000+x) = 13/100 * (15000+x)
=0.13 * (15000 + x)
= 1950 +0.13x

So the equation will be,
1800 + 0.15x = 1950 + 0.13x
Subtracting 0.13x on both sides

1800 + 0.02x = 1950
Subtracting 1800 on both sides

0.02x = 150
Divide by 0.02 on both sides

x = 150 / 0.02
x = 7500

Operation on Rational Numbers

Topic : Rational Numbers
Question : ADD 2/3 AND 3/4
Solution :
Step 1: Let us add 2/3 and ¾ 2/3+3/4
Step2: The denominators are not same hence find the LCM of
the denominators L.C.M=3x4=12
Step3: Convert the given rationals into rationals having common 2/3x4/4=8/12
denominators 3/4x3/3=9/12
Step4: Since the denominators are same add the numerators 8/12+9/12=8+9/12=7/12
Therefore 2/3+3/4=17/12

Question on Linear Equation

Topic : Base Ball Word Problem

Question : The rockets beat the tigers in a game of baseball, the rockets scored 4 more runs th the tigers the total number of runs was 14 . what was the score?

Solution:
Let the run scored by tigers be = x
Therefore the run scored by rockets = 4+x
Total runs (given) = 14
So now our equation is x+x+4=14
2x+4 = 14
2x = 14-4
2x = 10
x = 10/2
x= 5
Therore the run scored by tigers are 5
And run scored by rockets are (x+4)= (5+4)=9